In 3D a pyramid with a square base can be decomposed into the sum of two tetrahedra, i.e. two 3-simplices.
I am dealing with a homogeneous N-dimensional system of inequalities and my solution is a convex cone. I have in general M>=N vectors corresponding to extreme rays for this cone and I would like to would like to decompose this space into a sum of N-simplices. How do I do this whilst guaranteeing that I am not overcounting, i.e. that each point in the cone belongs to only one simplex?
My current idea is to choose all possible sets of N vectors from the M vectors but this is just a guess.
I apologise if this is a very easy question, or if it has already been answered on this site, but my background is not in geometry and I don't know what I should be searching for. I am asking here hoping that I will be steered in the right direction.